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Question

Find the value of a if the three equations are consistent
(a+1)3x+(a+2)3y=(a+3)3
(a+1)x+(a+2)y=a+3
x+y=1.

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Solution

Since the given equations are consistent,
a1a2=b1b2=c1c2......(a)

Considering the equations,
(a+1)3x+(a+2)3y=(a+3)3......(1)

(a+1)x+(a+2)y=(a+3).....(2)

From (a)

(a+1)3(a+1)=(a+2)3(a+2)=(a+3)3(a+3)

Considering 1st and 2nd terms, we have,

(a+1)3(a+1)=(a+2)3(a+2)

(a+1)2=(a+2)2

a2+2a+1=a2+4a+4

3=2a

a=32

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